Liverpool's Luis Suárez celebrates scoring his second goal against Sunderland during their Premier League match at the Stadium of Light. Photograph: Nigel Roddis/Reuters

Luis Suárez may have damaged Liverpool's "brand" when he sank his teeth into Chelsea's Branislav Ivanovic but the striker's return from a 10-game biting ban promises to do wonders for their Champions League ambitions as his side rose to second in the table.

Two comeback goals, one a simple tap in, the other an elegant swipe of the left foot, ensured that Suárez left precisely the right sort of mark on the sunny Wearside afternoon which staged his first Premier League appearance since April.

Managerless Sunderland did an awful lot right but even their own, impressive, prodigal son, Lee Cattermole – starting his first Premier League match since February – could not prevent them coming undone on the break and they remain stuck firmly to the bottom of the table. With one point from six games, Paolo Di Canio's replacement could do with the ability to turn water into wine.

Kevin Ball, in caretaker charge, covets the post but writing in the match programme, Margaret Byrne, Sunderland's chief executive, suggested the board are keeping their options open as to Di Canio's successor.

"We have already had contact with some interested parties and have others to speak to in the coming days," she wrote. "There is no definitive timescale on an appointment as we are carefully examining all available options. As soon as we have identified the right person we will make an announcement."

Ball began his audition brightly. His 4-2-3-1 formation seemed well configured to camouflage Sunderland's flaws and a starting XI featuring only three of the club's 14 summer signings offered Liverpool a few early frights. The most notable came when Sebastian Larsson's free-kick hit the bar with the returning Simon Mignolet beaten.

Even so Liverpool very nearly took the lead after Cattermole felled Daniel Sturridge just outside the box. When Keiren Westwood parried Steven Gerrard's free-kick, Martin Skrtel redirected the rebound beyond the goalkeeper but that effort was rightly disallowed for offside. Despite undeniably galvanising Ball's team, Cattermole was conceding a few too many free-kicks.

Nothing seems to be going quite right for Sunderland these days, an impression confirmed when Sturridge gave Liverpool the lead in somewhat fortuitous circumstances. Having narrowly failed to get his head to Gerrard's corner, the ball struck the top of the striker's arm and flew beyond Westwood. It was not deliberate and Howard Webb and his linesmen presumably assumed Sturridge had nudged what initially looked like a stooping header over the line but it seemed to serve as a microcosm of Sunderland's wretched luck of late.

Not that there was anything remotely flukey about Suárez's first goal. Sturridge's wonderful change of pace saw him accelerating on to Gerrard's raking long pass down the right and, with the defence left standing, the on-rushing Uruguayan met Sturridge's ball across the six-yard box. Within a millisecond he had polished things off courtesy of the simplest of close-range shots.

Although severely wounded by poor defending in the face of Gerrard's vision and Sturridge's pace, Sunderland were not being entirely outclassed. Pressing Liverpool high up the pitch, they hardly deserved to be two goals down on a day when Adam Johnson saw an ambitious curling shot curve fractionally off target and the otherwise unusually shaky Mignolet saved brilliantly from Craig Gardner with his legs following Cattermole's unexpectedly Xavi-esque subtle dinked pass.

At half-time Durham's County Championship winning team were warmly applauded on to the pitch. How Ellis Short, Sunderland's owner must have hoped some of their victorious aura might somehow rub off on his players.

Instead Suárez emerged looking even more inspired. Some high calibre movement and slick one-touch stuff from a forward clearly being fast forgiven for that summertime dalliance with Arsenal prompted Liverpool fans to sing: "Luis Suárez; he can bite who he wants."

It took Emanuele Giaccherini to silence them. The Italy winger, redeployed by Ball in a more central attacking role in the trio behind Jozy Altidore, shot Sunderland back into the game from close range after Mignolet could only parry Ki Sung -yueng's 25-yard shot. In the technical area, Ball pumped his fists.

Mignolet made an important save from Gardner but, continuing to press hard and high, Sunderland remained vulnerable to counterattacks. Carlos Cuéllar's last-ditch clearance denied Suárez and Westwood saved superbly from Kolo Touré.

The stage was set for Sturridge to break swiftly, cueing up Suárez to sweep home Liverpool's third with a stylish sidefoot. Ball looked as if he had been kicked in the teeth.